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arXiv · 2309.12268

A new renormalized volume type invariant

Jinyang Wu
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Abstract

In this paper, we define a new conformal invariant on complete non-compact hyperbolic surfaces that can be conformally compactified to bounded domains in $\mathbb{C}$. We study and compute this invariant up to one-connected surfaces. Our results give a new geometric criterion for choosing canonical representations of bounded domains in $\mathbb{C}$.

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Jinyang Wu. 2023-09-21. A new renormalized volume type invariant. https://doi.org/10.2140/pjm.2025.334.43

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